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By Freitas A.A.
This bankruptcy discusses using evolutionary algorithms, fairly genetic algorithms and genetic programming, in info mining and data discovery. We specialize in the knowledge mining activity of class. furthermore, we talk about a few preprocessing and postprocessing steps of the information discovery strategy, targeting characteristic choice and pruning of an ensemble of classifiers. We express how the necessities of information mining and data discovery impression the layout of evolutionary algorithms. specifically, we speak about how person illustration, genetic operators and health capabilities must be tailored for extracting high-level wisdom from info.
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Due to the various perturbations llcting on the system, one will usually not obtain exactly the same results when the same experiment is repeated; Ys is therefore a random vector. e. any p that corresponds to an optimal value of the cost function J, an estimate of p in the sense of j. 1 Least squares Quadratic cost functions are by far the most commonly used, since Gauss and Legendre (Stigler, ] 981), because of their intuitive appeal and relatively easy optimization (for LP models, the best estimate in the sense of a quadratic cost function can be obtained analytically, as will be seen in Chapler 4).
For example, to work with a relative error, it suffices to set Wik = 1IIYk(tik) I. 7. Note, however, that the estimate obtained may not be unique, even when a least-squares estimate would be. For instance, j(P) = Ipl + Ip - 31 is at its minimum over [0, 3]. 3. For a detailed presentation of the statistical properties of Lt estimators and of techniques LJU crtU'r/ll to compute them, one may consult (Bloomfield and Steiger. 1983; Dodge, 1987; Gonin and Money, 1989). 4. 3 Maximum likelihood The vector Pml will be a maximum-likelihood estimate if it maximizes the cm\l function If p were fixed, JI'y(ySlp) would be the probability density of the random vector yS being generated by a model with parameters p.
The maximum-likelihood method looks for the value of the parameter vector p that gives the highest likelihood to the observed data. This approach allows one to take into account in the design of the cost the available information on the nature of the noise acting on the system. In practice, it is often easier to look for by maximizing the log-likelihood function Pml which yields the same estimate since the logarithm function is monotonically increasing. ) according to a Gaussian law with mean Pi and variance We wish to estimate Pi and in the maximum-likelihood sense.